构造几何不敏感四边形膜元的广义协调方法

许多有限元模型在规则网格下具有很高的精度，但当网格畸变程度增大时，其计算精度也随之迅速下降．如何构造出对网格畸变不敏感的单元，长期以来是人们十分关注的课题．本文应用作者早期提出的广义协调方法，构造出具有平面内旋转自由度的任意四边形膜元．该单元不仅列式简洁，而且具有对网格畸变极不敏感的优异性能，为构造对网格畸变不敏感的优质单元提供了一个通用方法

A GENERALIZED CONFORMING QUADRILATERAL MEMBRANE ELEMENT INSENSITIVE TO GEOMETRIC DISTORTION

In numerical analysis many finite element models have acceptable performance when the computing meshes are regular. However, as the level of mesh distortion increases, their accuracy of solutions descends rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion was an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element proposed earlier by one of the author of this paper. The new element exhibits an excellent feature, that is, much less sensitive to geometric distortion. Also a general method to formulate high precision finite element that is less sensitive to geometric distortion is provided in this paper.